In his study of networks, Barabasi has put forth the dictum that everything touches everything. He says that the modernist practice of taking everything apart to examine its pieces does not guarantee that we will understand the way the pieces work when they are together – or that we will even ever understand how, exactly, to put them back together.
When one starts becoming familiar with different kinds of networks, they begin taking on particular characteristics that become obvious. They look like webs without spiders, wherein nodes are more or less connected but never solely responsible for maintaining connectivity.
Leonhard Euler is considered the grandfather of graph theory, but today, we consider his work our basis for thinking about networks. The 7 bridge coffeehouse problem demonstrated that
Graphs or networks have properties, hidden in their construction, that limit or enhance our ability to do things with them.
Every network display a separation of nodes between 2 and 14. Granovetter demonstrated the strength of weak ties, illuminating the importance of distributed connectivity.
Watts and Strogatz’s clustering model cracked Erdos and Renyi’s random worldview when it came to networks —> a random universe does not support connectors, or highly connected nodes which become network hubs.
A random network exhibits the familiar bell curve pattern and is likened to a highway map, with nodes evenly distributed which connect other nodes with relatively equal paths leading to and away from them. A scale-free network, on the other hand, does not exhibit a bell curve, but may have 2 or 3 giants for every hundred small nodes. It resembles more of a airway map, with some nodes handling much more traffic than others and servicing many, many other smaller nodes. These scale-free networks adhere to power laws, not “natural” laws.
Normally, bell curves (random networks) rule in nature, but when systems experience phase-transitions, the move from chaos to order occurs as components begin to self organize. This phenomenon produces scale-free networks containing hubs and adhering to power-laws.
80/20 and rich-get-richer – in scale-free networks, the connectors with the most links become hubs. Almost without exception, 20 percent of the nodes are connected to 80 percent of the links, making them hubs. Once they’re hubs, they keep collecting nodes, which is what is meant by rich-get-richer.
Real networks are governed by 2 laws: growth and preferential attachment. But growth alone can’t explain the emergence of power laws. The Fitness Model explains how new nodes get links when they come late to the game.
Scale-free networks experience a greater degree of disruption tolerance. The creators of ARPANET knew this, which is why the network was designed to enable it to function even if large portions of it were destroyed. When you have a web with no true spider, the web can survive even devastating destruction.
The structure of the web has an impact on everything – it “limits and determines our behavior in the online universe” (162).